{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TensorFlow Tutorial #01\n",
    "# Simple Linear Model\n",
    "\n",
    "by [Magnus Erik Hvass Pedersen](http://www.hvass-labs.org/)\n",
    "/ [GitHub](https://github.com/Hvass-Labs/TensorFlow-Tutorials) / [Videos on YouTube](https://www.youtube.com/playlist?list=PL9Hr9sNUjfsmEu1ZniY0XpHSzl5uihcXZ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "This tutorial demonstrates the basic workflow of using TensorFlow with a simple linear model. After loading the so-called MNIST data-set with images of hand-written digits, we define and optimize a simple mathematical model in TensorFlow. The results are then plotted and discussed.\n",
    "\n",
    "You should be familiar with basic linear algebra, Python and the Jupyter Notebook editor. It also helps if you have a basic understanding of Machine Learning and classification."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TensorFlow 2\n",
    "\n",
    "This tutorial was developed using TensorFlow v.1 back in the year 2016. There have been significant API changes in TensorFlow v.2. This tutorial uses TF2 in \"v.1 compatibility mode\", which is still useful for learning how TensorFlow works, but you would have to implement it slightly differently in TF2 (see Tutorial 03C on the Keras API). It would be too big a job for me to keep updating these tutorials every time Google's engineers update the TensorFlow API, so this tutorial may eventually stop working."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.metrics import confusion_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /home/magnus/anaconda3/envs/tf2/lib/python3.6/site-packages/tensorflow_core/python/compat/v2_compat.py:88: disable_resource_variables (from tensorflow.python.ops.variable_scope) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "non-resource variables are not supported in the long term\n"
     ]
    }
   ],
   "source": [
    "# Use TensorFlow v.2 with this old v.1 code.\n",
    "# E.g. placeholder variables and sessions have changed in TF2.\n",
    "import tensorflow.compat.v1 as tf\n",
    "tf.disable_v2_behavior()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This was developed using Python 3.6 (Anaconda) and TensorFlow version:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2.1.0'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tf.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The MNIST data-set is about 12 MB and will be downloaded automatically if it is not located in the given path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mnist import MNIST\n",
    "data = MNIST(data_dir=\"data/MNIST/\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The MNIST data-set has now been loaded and consists of 70.000 images and class-numbers for the images. The data-set is split into 3 mutually exclusive sub-sets. We will only use the training and test-sets in this tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of:\n",
      "- Training-set:\t\t55000\n",
      "- Validation-set:\t5000\n",
      "- Test-set:\t\t10000\n"
     ]
    }
   ],
   "source": [
    "print(\"Size of:\")\n",
    "print(\"- Training-set:\\t\\t{}\".format(data.num_train))\n",
    "print(\"- Validation-set:\\t{}\".format(data.num_val))\n",
    "print(\"- Test-set:\\t\\t{}\".format(data.num_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copy some of the data-dimensions for convenience."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The images are stored in one-dimensional arrays of this length.\n",
    "img_size_flat = data.img_size_flat\n",
    "\n",
    "# Tuple with height and width of images used to reshape arrays.\n",
    "img_shape = data.img_shape\n",
    "\n",
    "# Number of classes, one class for each of 10 digits.\n",
    "num_classes = data.num_classes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### One-Hot Encoding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output-data is loaded as both integer class-numbers and so-called One-Hot encoded arrays. This means the class-numbers have been converted from a single integer to a vector whose length equals the number of possible classes. All elements of the vector are zero except for the $i$'th element which is 1 and means the class is $i$. For example, the One-Hot encoded labels for the first 5 images in the test-set are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 0., 0., 0., 1., 0., 0.],\n",
       "       [0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 1., 0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.y_test[0:5, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need the classes as integers for various comparisons and performance measures. These can be found from the One-Hot encoded arrays by taking the index of the highest element using the `np.argmax()` function. But this has already been done for us when the data-set was loaded, so we can see the class-number for the first five images in the test-set. Compare these to the One-Hot encoded arrays above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 2, 1, 0, 4])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.y_test_cls[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper-function for plotting images"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function used to plot 9 images in a 3x3 grid, and writing the true and predicted classes below each image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_images(images, cls_true, cls_pred=None):\n",
    "    assert len(images) == len(cls_true) == 9\n",
    "    \n",
    "    # Create figure with 3x3 sub-plots.\n",
    "    fig, axes = plt.subplots(3, 3)\n",
    "    fig.subplots_adjust(hspace=0.3, wspace=0.3)\n",
    "\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        # Plot image.\n",
    "        ax.imshow(images[i].reshape(img_shape), cmap='binary')\n",
    "\n",
    "        # Show true and predicted classes.\n",
    "        if cls_pred is None:\n",
    "            xlabel = \"True: {0}\".format(cls_true[i])\n",
    "        else:\n",
    "            xlabel = \"True: {0}, Pred: {1}\".format(cls_true[i], cls_pred[i])\n",
    "\n",
    "        ax.set_xlabel(xlabel)\n",
    "        \n",
    "        # Remove ticks from the plot.\n",
    "        ax.set_xticks([])\n",
    "        ax.set_yticks([])\n",
    "        \n",
    "    # Ensure the plot is shown correctly with multiple plots\n",
    "    # in a single Notebook cell.\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot a few images to see if data is correct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the first images from the test-set.\n",
    "images = data.x_test[0:9]\n",
    "\n",
    "# Get the true classes for those images.\n",
    "cls_true = data.y_test_cls[0:9]\n",
    "\n",
    "# Plot the images and labels using our helper-function above.\n",
    "plot_images(images=images, cls_true=cls_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TensorFlow Graph\n",
    "\n",
    "The entire purpose of TensorFlow is to have a so-called computational graph that can be executed much more efficiently than if the same calculations were to be performed directly in Python. TensorFlow can be more efficient than NumPy because TensorFlow knows the entire computation graph that must be executed, while NumPy only knows the computation of a single mathematical operation at a time.\n",
    "\n",
    "TensorFlow can also automatically calculate the gradients that are needed to optimize the variables of the graph so as to make the model perform better. This is because the graph is a combination of simple mathematical expressions so the gradient of the entire graph can be calculated using the chain-rule for derivatives.\n",
    "\n",
    "TensorFlow can also take advantage of multi-core CPUs as well as GPUs - and Google has even built special chips just for TensorFlow which are called TPUs (Tensor Processing Units) that are even faster than GPUs.\n",
    "\n",
    "A TensorFlow graph consists of the following parts which will be detailed below:\n",
    "\n",
    "* Placeholder variables used to feed input into the graph.\n",
    "* Model variables that are going to be optimized so as to make the model perform better.\n",
    "* The model which is essentially just a mathematical function that calculates some output given the input in the placeholder variables and the model variables.\n",
    "* A cost measure that can be used to guide the optimization of the variables.\n",
    "* An optimization method which updates the variables of the model.\n",
    "\n",
    "In addition, the TensorFlow graph may also contain various debugging statements e.g. for logging data to be displayed using TensorBoard, which is not covered in this tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Placeholder variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Placeholder variables serve as the input to the graph that we may change each time we execute the graph. We call this feeding the placeholder variables and it is demonstrated further below.\n",
    "\n",
    "First we define the placeholder variable for the input images. This allows us to change the images that are input to the TensorFlow graph. This is a so-called tensor, which just means that it is a multi-dimensional vector or matrix. The data-type is set to `float32` and the shape is set to `[None, img_size_flat]`, where `None` means that the tensor may hold an arbitrary number of images with each image being a vector of length `img_size_flat`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = tf.placeholder(tf.float32, [None, img_size_flat])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we have the placeholder variable for the true labels associated with the images that were input in the placeholder variable `x`. The shape of this placeholder variable is `[None, num_classes]` which means it may hold an arbitrary number of labels and each label is a vector of length `num_classes` which is 10 in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_true = tf.placeholder(tf.float32, [None, num_classes])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we have the placeholder variable for the true class of each image in the placeholder variable `x`. These are integers and the dimensionality of this placeholder variable is set to `[None]` which means the placeholder variable is a one-dimensional vector of arbitrary length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_true_cls = tf.placeholder(tf.int64, [None])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variables to be optimized"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Apart from the placeholder variables that were defined above and which serve as feeding input data into the model, there are also some model variables that must be changed by TensorFlow so as to make the model perform better on the training data.\n",
    "\n",
    "The first variable that must be optimized is called `weights` and is defined here as a TensorFlow variable that must be initialized with zeros and whose shape is `[img_size_flat, num_classes]`, so it is a 2-dimensional tensor (or matrix) with `img_size_flat` rows and `num_classes` columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights = tf.Variable(tf.zeros([img_size_flat, num_classes]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second variable that must be optimized is called `biases` and is defined as a 1-dimensional tensor (or vector) of length `num_classes`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "biases = tf.Variable(tf.zeros([num_classes]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This simple mathematical model multiplies the images in the placeholder variable `x` with the `weights` and then adds the `biases`.\n",
    "\n",
    "The result is a matrix of shape `[num_images, num_classes]` because `x` has shape `[num_images, img_size_flat]` and `weights` has shape `[img_size_flat, num_classes]`, so the multiplication of those two matrices is a matrix with shape `[num_images, num_classes]` and then the `biases` vector is added to each row of that matrix.\n",
    "\n",
    "Note that the name `logits` is typical TensorFlow terminology, but other people may call the variable something else."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "logits = tf.matmul(x, weights) + biases"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now `logits` is a matrix with `num_images` rows and `num_classes` columns, where the element of the $i$'th row and $j$'th column is an estimate of how likely the $i$'th input image is to be of the $j$'th class.\n",
    "\n",
    "However, these estimates are a bit rough and difficult to interpret because the numbers may be very small or large, so we want to normalize them so that each row of the `logits` matrix sums to one, and each element is limited between zero and one. This is calculated using the so-called softmax function and the result is stored in `y_pred`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = tf.nn.softmax(logits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predicted class can be calculated from the `y_pred` matrix by taking the index of the largest element in each row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred_cls = tf.argmax(y_pred, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cost-function to be optimized"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make the model better at classifying the input images, we must somehow change the variables for `weights` and `biases`. To do this we first need to know how well the model currently performs by comparing the predicted output of the model `y_pred` to the desired output `y_true`.\n",
    "\n",
    "The cross-entropy is a performance measure used in classification. The cross-entropy is a continuous function that is always positive and if the predicted output of the model exactly matches the desired output then the cross-entropy equals zero. The goal of optimization is therefore to minimize the cross-entropy so it gets as close to zero as possible by changing the `weights` and `biases` of the model.\n",
    "\n",
    "TensorFlow has a built-in function for calculating the cross-entropy. Note that it uses the values of the `logits` because it also calculates the softmax internally."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "cross_entropy = tf.nn.softmax_cross_entropy_with_logits_v2(logits=logits,\n",
    "                                                           labels=y_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have now calculated the cross-entropy for each of the image classifications so we have a measure of how well the model performs on each image individually. But in order to use the cross-entropy to guide the optimization of the model's variables we need a single scalar value, so we simply take the average of the cross-entropy for all the image classifications."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost = tf.reduce_mean(cross_entropy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimization method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have a cost measure that must be minimized, we can then create an optimizer. In this case it is the basic form of Gradient Descent where the step-size is set to 0.5.\n",
    "\n",
    "Note that optimization is not performed at this point. In fact, nothing is calculated at all, we just add the optimizer-object to the TensorFlow graph for later execution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.5).minimize(cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance measures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need a few more performance measures to display the progress to the user.\n",
    "\n",
    "This is a vector of booleans whether the predicted class equals the true class of each image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "correct_prediction = tf.equal(y_pred_cls, y_true_cls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This calculates the classification accuracy by first type-casting the vector of booleans to floats, so that False becomes 0 and True becomes 1, and then calculating the average of these numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TensorFlow Run"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create TensorFlow session\n",
    "\n",
    "Once the TensorFlow graph has been created, we have to create a TensorFlow session which is used to execute the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "session = tf.Session()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialize variables\n",
    "\n",
    "The variables for `weights` and `biases` must be initialized before we start optimizing them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "session.run(tf.global_variables_initializer())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper-function to perform optimization iterations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 55.000 images in the training-set. It takes a long time to calculate the gradient of the model using all these images. We therefore use Stochastic Gradient Descent which only uses a small batch of images in each iteration of the optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function for performing a number of optimization iterations so as to gradually improve the `weights` and `biases` of the model. In each iteration, a new batch of data is selected from the training-set and then TensorFlow executes the optimizer using those training samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimize(num_iterations):\n",
    "    for i in range(num_iterations):\n",
    "        # Get a batch of training examples.\n",
    "        # x_batch now holds a batch of images and\n",
    "        # y_true_batch are the true labels for those images.\n",
    "        x_batch, y_true_batch, _ = data.random_batch(batch_size=batch_size)\n",
    "        \n",
    "        # Put the batch into a dict with the proper names\n",
    "        # for placeholder variables in the TensorFlow graph.\n",
    "        # Note that the placeholder for y_true_cls is not set\n",
    "        # because it is not used during training.\n",
    "        feed_dict_train = {x: x_batch,\n",
    "                           y_true: y_true_batch}\n",
    "\n",
    "        # Run the optimizer using this batch of training data.\n",
    "        # TensorFlow assigns the variables in feed_dict_train\n",
    "        # to the placeholder variables and then runs the optimizer.\n",
    "        session.run(optimizer, feed_dict=feed_dict_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper-functions to show performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dict with the test-set data to be used as input to the TensorFlow graph. Note that we must use the correct names for the placeholder variables in the TensorFlow graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "feed_dict_test = {x: data.x_test,\n",
    "                  y_true: data.y_test,\n",
    "                  y_true_cls: data.y_test_cls}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function for printing the classification accuracy on the test-set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_accuracy():\n",
    "    # Use TensorFlow to compute the accuracy.\n",
    "    acc = session.run(accuracy, feed_dict=feed_dict_test)\n",
    "    \n",
    "    # Print the accuracy.\n",
    "    print(\"Accuracy on test-set: {0:.1%}\".format(acc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function for printing and plotting the confusion matrix using scikit-learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_confusion_matrix():\n",
    "    # Get the true classifications for the test-set.\n",
    "    cls_true = data.y_test_cls\n",
    "    \n",
    "    # Get the predicted classifications for the test-set.\n",
    "    cls_pred = session.run(y_pred_cls, feed_dict=feed_dict_test)\n",
    "\n",
    "    # Get the confusion matrix using sklearn.\n",
    "    cm = confusion_matrix(y_true=cls_true,\n",
    "                          y_pred=cls_pred)\n",
    "\n",
    "    # Print the confusion matrix as text.\n",
    "    print(cm)\n",
    "\n",
    "    # Plot the confusion matrix as an image.\n",
    "    plt.imshow(cm, interpolation='nearest', cmap=plt.cm.Blues)\n",
    "\n",
    "    # Make various adjustments to the plot.\n",
    "    plt.tight_layout()\n",
    "    plt.colorbar()\n",
    "    tick_marks = np.arange(num_classes)\n",
    "    plt.xticks(tick_marks, range(num_classes))\n",
    "    plt.yticks(tick_marks, range(num_classes))\n",
    "    plt.xlabel('Predicted')\n",
    "    plt.ylabel('True')\n",
    "    \n",
    "    # Ensure the plot is shown correctly with multiple plots\n",
    "    # in a single Notebook cell.\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function for plotting examples of images from the test-set that have been mis-classified."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_example_errors():\n",
    "    # Use TensorFlow to get a list of boolean values\n",
    "    # whether each test-image has been correctly classified,\n",
    "    # and a list for the predicted class of each image.\n",
    "    correct, cls_pred = session.run([correct_prediction, y_pred_cls],\n",
    "                                    feed_dict=feed_dict_test)\n",
    "\n",
    "    # Negate the boolean array.\n",
    "    incorrect = (correct == False)\n",
    "    \n",
    "    # Get the images from the test-set that have been\n",
    "    # incorrectly classified.\n",
    "    images = data.x_test[incorrect]\n",
    "    \n",
    "    # Get the predicted classes for those images.\n",
    "    cls_pred = cls_pred[incorrect]\n",
    "\n",
    "    # Get the true classes for those images.\n",
    "    cls_true = data.y_test_cls[incorrect]\n",
    "    \n",
    "    # Plot the first 9 images.\n",
    "    plot_images(images=images[0:9],\n",
    "                cls_true=cls_true[0:9],\n",
    "                cls_pred=cls_pred[0:9])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper-function to plot the model weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function for plotting the `weights` of the model. 10 images are plotted, one for each digit that the model is trained to recognize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_weights():\n",
    "    # Get the values for the weights from the TensorFlow variable.\n",
    "    w = session.run(weights)\n",
    "    \n",
    "    # Get the lowest and highest values for the weights.\n",
    "    # This is used to correct the colour intensity across\n",
    "    # the images so they can be compared with each other.\n",
    "    w_min = np.min(w)\n",
    "    w_max = np.max(w)\n",
    "\n",
    "    # Create figure with 3x4 sub-plots,\n",
    "    # where the last 2 sub-plots are unused.\n",
    "    fig, axes = plt.subplots(3, 4)\n",
    "    fig.subplots_adjust(hspace=0.3, wspace=0.3)\n",
    "\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        # Only use the weights for the first 10 sub-plots.\n",
    "        if i<10:\n",
    "            # Get the weights for the i'th digit and reshape it.\n",
    "            # Note that w.shape == (img_size_flat, 10)\n",
    "            image = w[:, i].reshape(img_shape)\n",
    "\n",
    "            # Set the label for the sub-plot.\n",
    "            ax.set_xlabel(\"Weights: {0}\".format(i))\n",
    "\n",
    "            # Plot the image.\n",
    "            ax.imshow(image, vmin=w_min, vmax=w_max, cmap='seismic')\n",
    "\n",
    "        # Remove ticks from each sub-plot.\n",
    "        ax.set_xticks([])\n",
    "        ax.set_yticks([])\n",
    "        \n",
    "    # Ensure the plot is shown correctly with multiple plots\n",
    "    # in a single Notebook cell.\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance before any optimization\n",
    "\n",
    "The accuracy on the test-set is 9.8%. This is because the model has only been initialized and not optimized at all, so it always predicts that the image shows a zero digit, as demonstrated in the plot below, and it turns out that 9.8% of the images in the test-set happens to be zero digits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on test-set: 9.8%\n"
     ]
    }
   ],
   "source": [
    "print_accuracy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example_errors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance after 1 optimization iteration\n",
    "\n",
    "Already after a single optimization iteration, the model has increased its accuracy on the test-set significantly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimize(num_iterations=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on test-set: 22.2%\n"
     ]
    }
   ],
   "source": [
    "print_accuracy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example_errors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The weights can also be plotted as shown below. Positive weights are red and negative weights are blue. These weights can be intuitively understood as image-filters.\n",
    "\n",
    "For example, the weights used to determine if an image shows a zero-digit have a positive reaction (red) to an image of a circle, and  have a negative reaction (blue) to images with content in the centre of the circle.\n",
    "\n",
    "Similarly, the weights used to determine if an image shows a one-digit react positively (red) to a vertical line in the centre of the image, and react negatively (blue) to images with content surrounding that line.\n",
    "\n",
    "Note that the weights mostly look like the digits they're supposed to recognize. This is because only one optimization iteration has been performed so the weights are only trained on 100 images. After training on several thousand images, the weights become more difficult to interpret because they have to recognize many variations of how digits can be written."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_weights()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance after 10 optimization iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We have already performed 1 iteration.\n",
    "optimize(num_iterations=9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on test-set: 77.6%\n"
     ]
    }
   ],
   "source": [
    "print_accuracy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example_errors()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_weights()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance after 1000 optimization iterations\n",
    "\n",
    "After 1000 optimization iterations, the model only mis-classifies about one in ten images. As demonstrated below, some of the mis-classifications are justified because the images are very hard to determine with certainty even for humans, while others are quite obvious and should have been classified correctly by a good model. But this simple model cannot reach much better performance and more complex models are therefore needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We have already performed 10 iterations.\n",
    "optimize(num_iterations=990)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on test-set: 91.6%\n"
     ]
    }
   ],
   "source": [
    "print_accuracy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_example_errors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model has now been trained for 1000 optimization iterations, with each iteration using 100 images from the training-set. Because of the great variety of the images, the weights have now become difficult to interpret and we may doubt whether the model truly understands how digits are composed from lines, or whether the model has just memorized many different variations of pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_weights()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also print and plot the so-called confusion matrix which lets us see more details about the mis-classifications. For example, it shows that images actually depicting a 5 have sometimes been mis-classified as all other possible digits, but mostly as 6 or 8."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 958    0    1    4    0    7    5    2    3    0]\n",
      " [   0 1103    3    5    1    1    3    2   17    0]\n",
      " [   7    6  917   25   12    3    8   11   38    5]\n",
      " [   1    0   12  943    0   19    1   11   17    6]\n",
      " [   2    3    4    2  921    1    8    2    8   31]\n",
      " [  10    2    4   53    8  754   10    8   35    8]\n",
      " [  15    3    5    2   23   17  885    2    6    0]\n",
      " [   3    8   20    8    7    1    0  946    4   31]\n",
      " [   7    4    6   40    9   25    9   12  858    4]\n",
      " [  11    5    2   12   49    8    0   31   11  880]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_confusion_matrix()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now done using TensorFlow, so we close the session to release its resources."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This has been commented out in case you want to modify and experiment\n",
    "# with the Notebook without having to restart it.\n",
    "# session.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "\n",
    "These are a few suggestions for exercises that may help improve your skills with TensorFlow. It is important to get hands-on experience with TensorFlow in order to learn how to use it properly.\n",
    "\n",
    "You may want to backup this Notebook before making any changes.\n",
    "\n",
    "* Change the learning-rate for the optimizer.\n",
    "* Change the optimizer to e.g. `AdagradOptimizer` or `AdamOptimizer`.\n",
    "* Change the batch-size to e.g. 1 or 1000.\n",
    "* How do these changes affect the performance?\n",
    "* Do you think these changes will have the same effect (if any) on other classification problems and mathematical models?\n",
    "* Do you get the exact same results if you run the Notebook multiple times without changing any parameters? Why or why not?\n",
    "* Change the function `plot_example_errors()` so it also prints the `logits` and `y_pred` values for the mis-classified examples.\n",
    "* Use `sparse_softmax_cross_entropy_with_logits` instead of `softmax_cross_entropy_with_logits`. This may require several changes to multiple places in the source-code. Discuss the advantages and disadvantages of using the two methods.\n",
    "* Remake the program yourself without looking too much at this source-code.\n",
    "* Explain to a friend how the program works."
   ]
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    "## License (MIT)\n",
    "\n",
    "Copyright (c) 2016 by [Magnus Erik Hvass Pedersen](http://www.hvass-labs.org/)\n",
    "\n",
    "Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:\n",
    "\n",
    "The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.\n",
    "\n",
    "THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE."
   ]
  }
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